Difference between revisions of "Value of Ai'(0)"
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(Created page with "<div class="toccolours mw-collapsible mw-collapsed"> <strong>Theorem:</strong> The following formula holds: $$\mathrm{Ai}'(0)=-\dfrac{1}{3^{\frac{1}{3}}\Ga...") |
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$\mathrm{Ai}'(0)=-\dfrac{1}{3^{\frac{1}{3}}\Gamma\left(\frac{1}{3}\right)},$$ | $$\mathrm{Ai}'(0)=-\dfrac{1}{3^{\frac{1}{3}}\Gamma\left(\frac{1}{3}\right)},$$ | ||
where $\mathrm{Ai}$ denotes the [[Airy Ai]] function and $\Gamma$ denotes the [[gamma]] function. | where $\mathrm{Ai}$ denotes the [[Airy Ai]] function and $\Gamma$ denotes the [[gamma]] function. | ||
| − | + | ==Proof== | |
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Revision as of 07:58, 5 June 2016
Theorem
The following formula holds: $$\mathrm{Ai}'(0)=-\dfrac{1}{3^{\frac{1}{3}}\Gamma\left(\frac{1}{3}\right)},$$ where $\mathrm{Ai}$ denotes the Airy Ai function and $\Gamma$ denotes the gamma function.
